# Mass Formula for Light Nonstrange Mesons and Regge Trajectories in Quark Model

## TL;DR

This paper derives an analytical mass formula for light nonstrange mesons using a relativized quark model, predicting linear Regge trajectories and validating them against experimental meson spectra.

## Contribution

It introduces a new analytical mass formula for light mesons using the auxiliary field method, linking trajectory slopes to the confining parameter and strong coupling.

## Key findings

- Predicted quasi-linear Regge-Chew-Frautschi plots for excited states
- Trajectory slope inversely proportional to confining parameter a
- Good agreement with experimental meson spectra data

## Abstract

We study the Regge-like spectra of light mesons in a relativized quark model. An analytical mass formula is presented for the light unflavored mesons with the help of auxiliary field method, by which a quasi-linear Regge-Chew-Frautschi plot is predicted for the orbitally excited states. We show that the trajectory slope is proportional to the inverse confining parameter $1/a$ up to a factor depending on the strong coupling $\alpha_{s}$ when the orbital quantum number $L$ is large. The result is tested against the experimental data of the spectra of the meson families $\pi/b$,$\rho/a$,$\eta/h$ and $\omega/f$ in the ($L$,$M^{2}$) planes, with the fitted parameters consistent with that in the literatures.